One should not see the sacking of Ctesiphon as decisive or proof of Roman superiority in strategic terms. The Parthians had mostly cavalry forces and simply declined battle. The power base of the Parthians was in Iran, not Mesopotamia. This was beyond then reach of Rome, and thus they could not deliver a knock out blow. When the Romans withdrew, the Parthian army was still intact and quickly recaptured the lost territory.

Now, in terms of tactics, the Roman army was a very differrent beast in the 2nd Century compared to 53 BC. The army of Crassus was mostly of heavy infantry with little cavalry or missile support. It was the lack of archers which really led to the defeat, in my opinion. By the 2nd century Rome made full use of auxilliaries like light and heavy cavalry, skirmishers and missle troops. The Roman state was also far better organized with superior logistics. The Parthians recognized it was better to wait out the Romans rather than fight a pitched battle.

Sources

The Complete Roman Army, by Adrian Goldsworthy

Shadows in the Desert: Ancient Persia at War, by Kaveh Farrokh

You already got a pretty good answer but I think it should also be noted that Crassus was no Julius Caesar as far as tactical and strategic thinking goes:

He willfully decided to invade without Armenian support, trusted some not trustworthy guides, and lead his legions into terrain that he absolutely, positively had no business traveling though.

The Parthians were a mostly mounted army and he basically allowed his forces to be lead into the most open terrain around. His poor decision making stacked the deck against him from the start.

Even with all this, his army wasn’t even technically defeated in battle, the real damage was done after Crassus died in negotiations and the Romans had to turn tail and run home, being harried to death in the process. Before that they had suffered some major setbacks including the loss of most of their cavalry, but they were still a mostly intact army.

If a better man had lead the expedition, it might have gone very differently, but that’s neither here nor there. Fully mounted army’s would be something the Romans (and everyone else) would have trouble dealing with for a very long time after this period.

Rome was still in the process of subduing Gaul in 53 BC, so the Roman Empire was a much smaller creature (Egypt was still ruled by the Ptolemy dynasty, for example). Syria had only just been added to Rome by Pompey Magnus 10 years earlier. In the 2nd Century, those areas had been Roman for almost 200 years. There was a much better knowledge of the local terrain, the necessary logistics, and the type of combined arms needed to do well.

The Roman way of fighting superior enemies also frequently involved the construction of fortified camps (see Caesar's Bello Gallico) - A bit of the idea of making the enemy attack you on your terms. Crassus was rather wrong-footed and led into the desert by deceit, to a place where he was exposed and could be harassed by horse archers and couldn't build fortifications. His men were panicking and threatened to mutiny if he didn't parley (and were mostly new legions freshly raised, so perhaps not as tough). When Crassus did go to parley, he was killed.

The later expeditions were much better prepared and usually advanced down the Tigris and Euphrates, staying well supplied with materials by boat. That allowed the construction of fortifications and of siege equipment when needed, and also had much stronger cavalry.

Related question: I’ve read Crassus sent his main cavalry far ahead of the formation which allowed them to be ambushed and defeated, leaving the army mostly without cavalry. Is this true? And had he not done this would the battle have gone the way it did?